中国科学院数学与系统科学研究院

数学研究所

调和分析及其应用研究中心

学术报告

调和分析和偏微分方程研讨班

报告人：张景宣（清华大学）

题  目： Localization estimates for quantum dynamics: sub-ballistic transport

时  间：2024.10.14（星期一）16：00-17：00

地  点：思源楼S803

摘  要：Sub-ballistic transport refers to the phenomenon that particles move at strictly sub-linear rate in a dynamical system. This phenomenon has been observed in various nonequilibrium quantum lattice models, with Hamiltonians such as the Fibonacci operator and the almost Mathieu operator (Damanik-Tcheremchantsev, JAMS 2004). In this talk, we present sub-ballistic transport bounds for generic non-autonomous Schrödinger operators on lattices of arbitrary dimension. The main condition is that momentum vanishes sufficiently fast in the front of the wavepackets. The results apply to long-range Hamiltonian with polynomial decaying off-diagonal terms and can be extended, via a frozen-coefficient argument, to generic discrete nonlinear Schrödinger equations. Based on joint works with M. Lemm, S. Rademacher, and C. Rubliliani.